First difference of spread is regressed on value weighted average of first difference of spread for the market and value weighted market return.

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For Equation 3 and Equation 4, we expect to see different results compared to Equation 1 and Equation 2 respectively. The bias should not necessarily result in lower (or higher) levels of commonality. The bias is in the liquidity measure’s change from time t to t+1. We simply argue that such bias could have impact on commonality estimations (or any liquidity study). Howev- er, we expect that the difference in level of commonality between estimations using percen- tage change and first difference should be lower for most liquid equity markets. The difference should be more visible for lower liquidity markets (where variance of daily liquidity is high).

For further tests of commonality, we will be using Equation 4 as our base model in which we test first difference of liquidity measure with value weighted market variables.

Controlling for day-of-the-week effect

In order to test for the impact of day-of-the-week effect on commonality in liquidity, we include four daily dummies to Equation 4.

, - )& -. )& / -0 )&

-₁ )& -₂ )& _/ -₃ )& -₄ .

-6 7 -8 7. -9 71 - 72 5

Equation 5: First difference of spread is regressed on value weighted average of first difference of spread for the market, value weighted market return and four daily dummies.

In this equation, D1is a dummy variable which equals to 1 if the day is a Monday. D2is the dummy variable for Tuesday. D4is the dummy variable for Thursday. D5is the dummy variable for Friday. While it is suggested in previous literature that there may be persistent day-of-the- week effect for liquidity, we do not expect to see much change in commonality levels between different weekdays. While liquidity levels may change for different days, stocks’ change in li-

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quidity sensitivity is not expected to be any different on different weekdays. However, day-of- the-week effect in liquidity is reported in earlier literature, it is reported to be persistent and more common in emerging markets (or less liquid markets), we would like to test for its effect on our further examination of commonality factors. In case of no change in commonality le- vels, we will not be including them in our further tests.

Controlling for market direction

With this hypothesis we are examining whether the proportion of statistically significant liquidity sensitivity betas within the market is the same in down and up markets. The discus- sion about the underlying sources of commonality emphasized on inventory cost and asymme- tric information explanations. For the dealer markets, inventory cost is borne by the market makers. For the auction markets, any trader carrying a large intraday volume will bear some inventory cost. Market makers will caution themselves against any adverse market move- ments. As long as their goal is to have turnover and to earn bid-ask spread, keeping high inven- tory levels is undesirable. Any order imbalance will eventually distract inventory balance and lead to increased transaction costs. It is argued by Chordia, Roll, and Subrahmanyam (2001) that change in transaction costs occur in a different rate in down and up markets. This may be explained by the investors’ willingness to wait for more profits while the market is increasing and their impatience when there are increasing losses. The difference between the panic state versus patience state leads to order imbalances between down markets and up markets. Also, short-selling constraints and margin considerations are more likely to be binding during down markets.

We define down markets as any trading day with a negative return and up market as any trading day with a non-negative return. In order to test our hypothesis that commonality dif-

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fers for down and up markets, we include a dummy variable (UD) to Equation 4, which is equal to one if the market is non-negative.

, - )& -. )& / -0 )&

-₁ )& -₂ )& _/ -₃ )& -₄ .

-₆ :7 5

Equation 6: First difference of spread is regressed on value weighted average of first difference of spread for the market, value weighted market return and market direction dummy.

The overreaction of investors during down markets leads to order imbalances and there- fore leads to increased transaction costs. This increase should have general effect on all shares. Thus the market and the shares that make up the market will have a tendency to move together towards lower liquidity. Thus, we expect the down markets to be characterized with positive liquidity betas that are close to one. On the other hand, the underreaction of investors during up markets also leads to order imbalances. However, the difference of transaction costs due to under- and over-reactions will not be the same. Accordingly, we expect to have larger commonality (higher proportion of statistically significant liquidity betas) in down markets compared to up markets. We also expect to have higher proportion of positive liquidity betas (and closer to one) in down markets compared to up markets.

In terms of comparison between emerging and developed markets, market crashes follow- ing consistent negative market returns are more common in emerging markets. The increases in transaction costs due to order imbalances are also larger in emerging markets. High market depth and high transaction volume would allow developed markets to have more sustainabili- ty. These markets have larger number of participants which may not under- or over-react to

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the same extent. The existence of institutional investors in higher numbers and larger stakes in developed markets make them less prone to panic sales. The historic evidence of availability of liquidity (at least compared to emerging markets) also makes developed markets more relia- ble. For an investor, a down market bears more reasons to panic for emerging markets than it does for developed markets. For the up markets however, the differences may not be as dis- tinct. The main difference between emerging and developed markets would be the short-sale restrictions in emerging markets. These restrictions (where exists) would ensure that there are no panic purchases in up markets with similar motives to panic sales in down markets. Thus, emerging markets, in up markets, would have more reasons to be patient and under-react. Accordingly, we expect that the emerging markets will have more overreaction in down mar- kets compared to developed markets. They will also have more under-reaction in up markets. Thus, we expect increased commonality in liquidity in down markets especially in emerging markets.

Controlling for autoregressive component

It is quite common for returns to have autoregressive components. Based on the relation- ship between return and liquidity, we expect to have autoregressive component in liquidity measures as well. Furthermore, since it is theoretically argued that commonality is due to market-makers’ (and investors) inventory concerns or asymmetric information, it is a natural result to see market-makers (or investors) to start the trading day with previous day’s invento- ry and some asymmetric information spillover from previous day. In terms of maker-maker (or investor) behavior in trading, it is also natural to expect relative trading behavior in trading to previous day. In other words, trader would have already established perceptions about specific stocks early in the day based on previous day’s trading. In order to test the impact of autore-

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gressive components for commonality in liquidity, we include the lag of first difference of spread to Equation 4.

, - )& -. )& / -0 )&

-₁ )& -₂ )& _/ -₃ )& -₄ .

-₆ 5

Equation 7: First difference of spread is regressed on value weighted average of first difference of spread for the market, value weighted market return and lag of first difference of spread.

While we believe that including lagged value of the liquidity measure would improve the reliability of the estimation, considering liquidity has autoregressive component, its effect on commonality should not be considerable. The main argument is the fact that predispositions about stocks’ liquidity should be ongoing and could be considered sticky. Thus, we would ex- pect to have certain characteristics of stocks resulting in different trading patterns for market- makers and traders. Thus, their short-term perceptions should not be deterministic in stocks’ long term commonality with market liquidity.

Other liquidity measures

While the previous tests were based on the spread, we also estimated commonality using other liquidity measures such as proportional spread, effective spread, proportional effective spread and percentage spread. While related previous literature for commonality in liquidity does not report much different results between different measures of liquidity, we test for commonality for these measures as well for robustness purposes. The following four models are based on Equation 4 with suggested different liquidity measures.

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, - )& -. )& / -0 )&

-₁ )& -₂ )& _/ -₃ )& -₄ .

5

Equation 8: First difference of proportional spread is regressed on value weighted average of first difference of